The structural connectome has emerged as a powerful tool to characterize the network architecture of the human brain and shows great potential for generating important new biomarkers for neurologic and psychiatric disorders. The edges of the cerebral graph traverse white matter to interconnect cortical and subcortical nodes, although the anatomic embedding of these edges is generally overlooked in the literature. Mapping the paths of the connectome edges could elucidate the relative importance of individual white matter tracts to the overall network topology of the brain and also lead to a better understanding of the effect of regionally-specific white matter pathology on cognition and behavior. In this work, we introduce edge density imaging (EDI), which maps the number of network edges that pass through every white matter voxel. Test-retest analysis shows good to excellent reliability for edge density (ED) measurements, with consistent results using different cortical and subcortical parcellation schemes and different diffusion MR imaging acquisition parameters. We also demonstrate that ED yields complementary information to both traditional and emerging voxel-wise metrics of white matter microstructure and connectivity, including fractional anisotropy, track density, fiber orientation dispersion and neurite density. Our results demonstrate spatially ordered variations of ED throughout the white matter, notably including greater ED in posterior than anterior cerebral white matter. The EDI framework is employed to map the white matter regions that are enriched with pathways connecting rich club nodes and also those with high densities of intra-modular and inter-modular edges. We show that periventricular white matter has particularly high ED and high densities of rich club edges, which is significant for diseases in which these areas are selectively affected, ranging from white matter injury of prematurity in infants to leukoaraiosis in the elderly. Using edge betweenness centrality, we identify specific white matter regions involved in a large number of shortest paths, some containing highly connected rich club edges while others are relatively isolated within individual modules. Overall, these findings reveal an intricate relationship between white matter anatomy and the structural connectome, motivating further exploration of EDI for biomarkers of cognition and behavior.